Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in JAVA):

Solution:

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        double h = sc.nextInt();
        S = h / 2 / n;
        for (int i = 1; i < n; i++) {
            double b = bin(h,i);
            System.out.printf("%.9f", b );

            System.out.print(" ");
        }

    }

    static double S;

    static double bin(double h, int k) {
        double start = 0;
        double end = h;
        double ans = (start + end) / 2;
        while (start + 0.0000001 < end) {
            if (ans / h * ans / 2 > S * k) {
                end = ans;
            } else {
                start = ans;
            }
            ans = (start + end) / 2;
        }
        return ans;
    }

    static class Timeline implements Comparable<Timeline> {
        int money;
        int id;

        @Override
        public int compareTo(Timeline o) {
            if (money != o.money) return o.money - money;
            return id - o.id;

        }
    }
}